Model of a relativistic oscillator in a generalized Schrödinger picture

In a generalized Schrödinger picture, we consider the motion of a relativistic particle in an external field (like in the case of a harmonic oscillator). In this picture the analogs of the Schrödinger operators of the particle are independent of both the time and the space coordinates. These operators induce operators which are related to Killing vectors of the Anti de Sitter (AdS) space. We also consider the nonrelativistic limit.